`f(x) = (((2x + 3)^2)(x - 2)^5)/((x^3)(x - 5)^2)` Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values.
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Vertical asymptotes are the undefined points, also known as zeros of denominator.
Let's find the zeros of denominator of the function,
Vertical Asymptotes are x=0 , x=5
For Horizontal Asymptotes
Degree of Numerator of the function=7
Degree of Denominator of the function=5
Degree of Numerator`>` 1+Degree of Denominator
`:.` There is no Horizontal Asymptote
Now let's find intercepts
x intercepts can be found when f(x)=0
`2x+3=0 , x-2=0`
`x=-3/2 , x=2`
So x intercepts are -1.5 and 2.
Since x is undefined at x=0 , there are no y intercepts.
See the attached graph and link.
From the graph,
f(8) `~~` 600``
No Local Maximum
Minimum at `(-1.5,0)`
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